The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913555908919296 |
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| author | Gürkanlı, A. Turan |
| author_facet | Gürkanlı, A. Turan |
| contents | In \cite{g5}, we defined and investigated the grand Wiener amalgam space $W(L^{p),θ_1}(Ω), L^{q),θ_2}(Ω))$ , where $1<p,q<\infty, θ_1>0, θ_2>0$, $Ω\subset\mathbb R^{n} $ and the Lebesgue measure of $Ω$ is finite. In the present paper we generalize this space and define the generalized grand Wiener amalgam space $W(L_{a}^{p)}(\mathbb R^{n}), L_{b}^{q)}(\mathbb R^{n})),$ where $L_{a}^{p)}(\mathbb R^{n})$ and $L_{b}^{q)}(\mathbb R^{n}),$ are the generalized grand Lebesgue spaces, (see \cite{u}, \cite{su3}). Later we investigate some basic properties. Next we study embeddings for these spaces and we discuss boundedness and unboundedness of the Hardy-Littlewood maximal operator between some generalized grand Wiener amalgam spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators Gürkanlı, A. Turan Functional Analysis In \cite{g5}, we defined and investigated the grand Wiener amalgam space $W(L^{p),θ_1}(Ω), L^{q),θ_2}(Ω))$ , where $1<p,q<\infty, θ_1>0, θ_2>0$, $Ω\subset\mathbb R^{n} $ and the Lebesgue measure of $Ω$ is finite. In the present paper we generalize this space and define the generalized grand Wiener amalgam space $W(L_{a}^{p)}(\mathbb R^{n}), L_{b}^{q)}(\mathbb R^{n})),$ where $L_{a}^{p)}(\mathbb R^{n})$ and $L_{b}^{q)}(\mathbb R^{n}),$ are the generalized grand Lebesgue spaces, (see \cite{u}, \cite{su3}). Later we investigate some basic properties. Next we study embeddings for these spaces and we discuss boundedness and unboundedness of the Hardy-Littlewood maximal operator between some generalized grand Wiener amalgam spaces. |
| title | The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2408.02406 |